2002. 
Josh writes the numbers . He marks out , skips the next number , marks out , and continues skipping and marking out the next number to the end of the list. Then he goes back to the start of his list, marks out the first remaining number , skips the next number , marks out , skips , marks out , and so on to the end. Josh continues in this manner until only one number remains. What is that number?
This problem is copyrighted by the American Mathematics Competitions.

Instructions for entering answers:
For questions or comments, please email markan@eudelic.com.
Try our new, free contest math practice test. All new, neverseenbefore problems.
I offer online AMC/AIME classes periodically. Join the mailing list to be informed next time they're offered.
Private coaching is also available.